Simulation and jack-knifing assessment of home-range indices based on underlying trajectories

1. Home-range indices. describing, the area over which an animal moves or within which it concentrates its activity, are widely used in the analysis of animal movement, habitat selection, interaction and survival. the basic topics of applied animal ecology. However, the wide range of available indices and a poor understanding of their statistical properties limits their applicability, their interpretation and the ease by which comparisons can be made. These restrict many analyses to qualitative rather than quantitative assessments of home-range. We present an analysis of home-range indices under different conditions to assess their relative performance quantitatively. and we suggest a method of correcting for biases to allow quantitative comparisons between studies and techniques. 2. We compared the performance of a range of current home-range indices against the underlying animal trajectory. A moving animal describes a trajectory, a continuo us line of movement through space and time. Home-range is redefined as an outline enclosing a specified proportion of the trajectory over a specified period, This definition allows the performance of different home-range indicts to be compared quantitatively. 3. Detailed radiotracking data from a chaffinch Fringilla coelebs L. and a goshawk Accipiter gentilis L. were used to reconstruct trajectories. intermittent radiotracking was simulated by randomly extracting 200 sets, each of 30, 100 and 500 fixes for each animal. Seven home-range indices were used to generate home-range outlines at nominal 20%, 30%, 40%, 50%, 60%, 70%, 80%, 85%, 90%, 95% and 100% cores. 4. The area estimates, mean/variance ratio of area, overlap, percentage inclusion of trajectory, and trajectory density within each outline were used to compare the effectiveness of techniques and their ability to provide quantitative measures of animal use. 5. No technique performed well under all criteria. There was a spectrum of performance from techniques producing outlines with high trajectory density, low spatial stability and high sensitivity to sample size; to low trajectory density, high spatial stability and low sensitivity to sample size. 6. The nominal percentage cores produced by the techniques did not reflect accurately the true percentage time spent within that outline. A jack-knifing technique was evaluated that calibrates the true percentage cores at each nominal level for any home-range index. Suggestions are made for the quantitative interpretation of current indices, the use of different indices for specific analyses, and the development of new fix- and trajectory-based indices.